In the context of BNNs most popular choice to replace the sampling from the posterior is Hamiltonian MC (HMC) [1]}, [2]}, also known as hybrid Monte Carlo, which method uses the derivatives of the density function being sampled to generate efficient transitions spanning the posterior.
HMC uses an approximate Hamiltonian dynamics simulation based on numerical integration which is then corrected by performing a Metropolis acceptance step.
Unfortunately, HMC does not scale to large datasets, because it is inherently a batch algorithm—it requires visiting the entire training set for every update.
